If the humidity is high enough to cause respiratory distress, none of those cats should be confined in that room, & I don't know that Clavamox will help;
it's an anti-biotic & won't help fungal or bacterial infection.

I'd take that cat to the vet right this minute.

I wish you the best.

Any type of stress can cause all kinds of problems in cats including urinary problems and respiratory problems. Humidity isn't usually an issue by itself- there are millions of cats living outdoors in the tropics without problems. But if there is mold or other allergens because of high humidity that could be a major problem to allergic cats.